Fixed Point Four-Fermi Theories

Abstract

I review dynamical chiral symmetry breaking in four-fermi models, including results of Monte Carlo simulations with dynamical fermions. For 2<d<4, where the phase transition defines an ultraviolet fixed point of the renormalisation group, the continuum theory may either be describable using the large-N_f expansion, as in the case of the Gross-Neveu model, or be intrinsically non-perturbative, as in the case of the Thirring model. For d=4, the models are trivial and are described by a mean field equation of state with logarithmic corrections to scaling, which may nonetheless define new universality classes distinct from those of ferromagnetism.

arXiv comment19 pages LaTeX, contribution to the 1st APCTP-ICTP Joint International Conference on Recent Developments in Non-Perturbative Methods, May 1997, Seoul, Korea

Cited by in corpus (2)

• Large-$N$ Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect
• The Perturbative Gross Neveu Model Coupled to a Chern-Simons Field: A Renormalization Group Study